PH-UY 1013 Mechanics: Syllabus and Study Guide

PH-UY 1013 Mechanics: Course Syllabus and Study Notes

I. Introduction to PH-UY 1013 Mechanics

This course is the first in a sequence of three physics courses designed for engineering and science majors. It introduces the fundamental principles of mechanics, providing a foundation for further study in physics and related fields.

• Course Focus: Understanding the motion of particles and systems, forces, energy, and related physical laws.

• Credit Hours: 3 credits (three hours per week for lectures, one hour per week for recitation).

• Prerequisites: MA-UY 1024 or equivalent (Calculus I).

II. Main Topics Covered

The syllabus outlines the following major topics, each essential for mastering classical mechanics:

• Vectors

• One-Dimensional Motion

• Two-Dimensional Motion

• Newton's Laws of Motion

• Circular Motion

• Work and Energy

• Energy Conservation

• Momentum and Collisions

• Rotational Motion

• Angular Momentum

• Statics

• Gravity

• Oscillations

III. Course Objectives

The course aims to develop students' understanding of the following:

• Basic Principles: Conservation of energy, momentum, and the concept of forces.

• Mathematical Skills: Application of algebra, trigonometry, and calculus to solve physics problems.

• Kinematics: Description of motion in one, two, and three dimensions, including velocity, acceleration, and displacement.

• Work, Energy, and Power: Understanding work, energy transfer, and power in physical systems.

• Impulse and Momentum: Conservation laws and their application to collisions and explosions.

• Rotational Motion: Analysis of rotating systems, including angular velocity and torque.

• Gravitation: Application of Newton's law of gravitation to solve problems involving planetary motion.

• Harmonic Motion: Study of oscillatory systems and their properties.

• Problem Solving: Development of strong analytical and quantitative skills.

IV. Key Definitions and Concepts

• Vector: A quantity with both magnitude and direction, used to represent displacement, velocity, acceleration, and force.

• Kinematics: The study of motion without considering its causes.

• Newton's Laws of Motion:

  1. First Law (Inertia): An object remains at rest or in uniform motion unless acted upon by a net external force.

  2. Second Law: The net force on an object is equal to the mass times its acceleration. $F = ma$

  3. Third Law: For every action, there is an equal and opposite reaction.

• Work: The product of force and displacement in the direction of the force. $W = F \cdot d \cdot \cos\theta$

• Energy: The capacity to do work. Kinetic energy is given by: $K = \frac{1}{2}mv^2$

• Conservation of Energy: Energy cannot be created or destroyed, only transformed.

• Momentum: The product of mass and velocity. $p = mv$

• Impulse: Change in momentum due to a force applied over time. $J = F \Delta t$

• Rotational Motion: Motion of objects around a fixed axis, characterized by angular velocity ($\omega$) and angular acceleration ($\alpha$).

• Torque: A measure of the force causing an object to rotate. $\tau = r F \sin\theta$

• Gravitational Force: The attractive force between two masses. $F_g = G \frac{m_1 m_2}{r^2}$

• Simple Harmonic Motion: Oscillatory motion where the restoring force is proportional to displacement. $F = -kx$

V. Example Applications

• Projectile Motion: Calculating the trajectory of an object under gravity.

• Collisions: Analyzing elastic and inelastic collisions using conservation of momentum.

• Rotational Dynamics: Determining the angular acceleration of a rotating disk under applied torque.

• Oscillations: Studying the motion of a mass-spring system.

VI. Course Schedule Overview

The following table summarizes the weekly topics and assignments:

Week	Lecture Topics	Recitation/Assignments
1	Intro and Units	Recitation
2	Vectors	HW1 due
3	One Dimensional Motion	HW2 due
4	Two Dimensional Motion	HW3 due
5	Newton's Laws	HW4 due
6	Circular Motion	HW5 due
7	Work and Energy	HW6 due
8	Energy Conservation; Momentum and Collisions	HW7 due
9	Momentum and Collisions (cont.); Rotations	HW8 due
10	Rotation (cont.); Angular Momentum	HW9 due
11	Angular Momentum (cont.); Statics	HW10 due
12	Statics (cont.); Gravity	HW11 due
13	Gravity (cont.); Oscillations	HW12 due

Additional info: The schedule includes midterm and final exams, as well as weekly quizzes and homework assignments. The lowest two quiz and homework grades are dropped.

VII. Grading Policy

The course uses a "best-of" grading system, with the following breakdown:

Component	Percentage
Homework	5%
Quizzes	10%
Midterm	30%
Final Exam	35%
Participation	5%
Best-of	15%

Letter grades are assigned according to the following scale:

Letter Grade	Numerical Range
A	90.0% - 100%
B+	87.5% - 90.0%
B	82.5% - 87.5%
B-	80.0% - 82.5%
C+	77.5% - 80.0%
C	72.5% - 77.5%
C-	70.0% - 72.5%
D	50.0% - 70.0%
F	Below 50.0%

VIII. Academic Support and Resources

• Recitation: Weekly sessions for clarifying concepts and solving problems.

• Online Resources: Course materials available on Brightspace and WebAssign.

• Study Help: The Polytechnic Tutoring Center offers free tutoring for first- and second-year students.

• Textbook: "Physics for Scientists & Engineers" (11th Edition) by Serway, Jewett, and Peroomian.

IX. Academic Policies

• Makeup and Extensions: Provided only for documented emergencies.

• Academic Honesty: All students must adhere to university policies regarding academic integrity.

• Student Advocacy: Support available for mental health, personal issues, and disabilities.

• Inclusion Statement: Commitment to diversity and equitable environment for all students.

• Policy on Use of AI: AI tools may be used for homework assistance, but not for quizzes or exams.

X. Summary Table: Weekly Topics and Assignments

Week	Lecture Topic	Assignment Due
1	Intro and Units	HW1
2	Vectors	HW2
3	One Dimensional Motion	HW3
4	Two Dimensional Motion	HW4
5	Newton's Laws	HW5
6	Circular Motion	HW6
7	Work and Energy	HW7
8	Energy Conservation; Momentum and Collisions	HW8
9	Momentum and Collisions (cont.); Rotations	HW9
10	Rotation (cont.); Angular Momentum	HW10
11	Angular Momentum (cont.); Statics	HW11
12	Statics (cont.); Gravity	HW12
13	Gravity (cont.); Oscillations	HW13

Additional info: The syllabus also includes policies on attendance, grading, academic honesty, and student support services, ensuring a comprehensive and supportive learning environment for all students.